0.10/1.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/1.12 % Command : run_E %s %d THM 0.11/1.50 % Computer : n014.cluster.edu 0.11/1.50 % Model : x86_64 x86_64 0.11/1.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/1.50 % Memory : 8042.1875MB 0.11/1.50 % OS : Linux 3.10.0-693.el7.x86_64 0.11/1.50 % CPULimit : 1440 0.11/1.50 % WCLimit : 180 0.11/1.50 % DateTime : Thu Jul 4 08:31:40 EDT 2024 0.11/1.52 % CPUTime : 0.27/2.79 Running higher-order theorem proving 0.27/2.84 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p 1.04/3.16 # Version: 3.2.0-ho 1.04/3.16 # Preprocessing class: HSLMSLSSLLLCHSA. 1.04/3.16 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 1.04/3.16 # Starting ho_unfolding_5 with 720s (4) cores 1.04/3.16 # Starting pre_casc_3 with 180s (1) cores 1.04/3.16 # Starting new_ho_10_cnf2 with 180s (1) cores 1.04/3.16 # Starting full_lambda_10 with 180s (1) cores 1.04/3.16 # Starting ehoh_best_nonlift_rwall with 180s (1) cores 1.04/3.16 # ho_unfolding_5 with pid 14922 completed with status 0 1.04/3.16 # Result found by ho_unfolding_5 1.04/3.16 # Preprocessing class: HSLMSLSSLLLCHSA. 1.04/3.16 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 1.04/3.16 # Starting ho_unfolding_5 with 720s (4) cores 1.04/3.16 # No SInE strategy applied 1.04/3.16 # Search class: HGHSM-FSLM32-MHSMMSBN 1.04/3.16 # Scheduled 12 strats onto 4 cores with 720 seconds (720 total) 1.04/3.16 # Starting full_lambda_5 with 59s (1) cores 1.04/3.16 # Starting ho_unfolding_5 with 73s (1) cores 1.04/3.16 # Starting pre_casc_4 with 59s (1) cores 1.04/3.16 # Starting pre_casc_3 with 59s (1) cores 1.04/3.16 # pre_casc_4 with pid 14931 completed with status 0 1.04/3.16 # Result found by pre_casc_4 1.04/3.16 # Preprocessing class: HSLMSLSSLLLCHSA. 1.04/3.16 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 1.04/3.16 # Starting ho_unfolding_5 with 720s (4) cores 1.04/3.16 # No SInE strategy applied 1.04/3.16 # Search class: HGHSM-FSLM32-MHSMMSBN 1.04/3.16 # Scheduled 12 strats onto 4 cores with 720 seconds (720 total) 1.04/3.16 # Starting full_lambda_5 with 59s (1) cores 1.04/3.16 # Starting ho_unfolding_5 with 73s (1) cores 1.04/3.16 # Starting pre_casc_4 with 59s (1) cores 1.04/3.16 # Preprocessing time : 0.005 s 1.04/3.16 # Presaturation interreduction done 1.04/3.16 1.04/3.16 # Proof found! 1.04/3.16 # SZS status Theorem 1.04/3.16 # SZS output start CNFRefutation 1.04/3.16 thf(decl_22, type, in: $i > $i > $o). 1.04/3.16 thf(decl_23, type, exu: ($i > $o) > $o). 1.04/3.16 thf(decl_24, type, setextAx: $o). 1.04/3.16 thf(decl_25, type, emptyset: $i). 1.04/3.16 thf(decl_26, type, emptysetAx: $o). 1.04/3.16 thf(decl_27, type, setadjoin: $i > $i > $i). 1.04/3.16 thf(decl_28, type, setadjoinAx: $o). 1.04/3.16 thf(decl_29, type, powerset: $i > $i). 1.04/3.16 thf(decl_30, type, powersetAx: $o). 1.04/3.16 thf(decl_31, type, setunion: $i > $i). 1.04/3.16 thf(decl_32, type, setunionAx: $o). 1.04/3.16 thf(decl_33, type, omega: $i). 1.04/3.16 thf(decl_34, type, omega0Ax: $o). 1.04/3.16 thf(decl_35, type, omegaSAx: $o). 1.04/3.16 thf(decl_36, type, omegaIndAx: $o). 1.04/3.16 thf(decl_37, type, replAx: $o). 1.04/3.16 thf(decl_38, type, foundationAx: $o). 1.04/3.16 thf(decl_39, type, wellorderingAx: $o). 1.04/3.16 thf(decl_40, type, descr: ($i > $o) > $i). 1.04/3.16 thf(decl_41, type, descrp: $o). 1.04/3.16 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_43, type, dsetconstrI: $o). 1.04/3.16 thf(decl_44, type, dsetconstrEL: $o). 1.04/3.16 thf(decl_45, type, dsetconstrER: $o). 1.04/3.16 thf(decl_46, type, exuE1: $o). 1.04/3.16 thf(decl_47, type, prop2set: $o > $i). 1.04/3.16 thf(decl_48, type, prop2setE: $o). 1.04/3.16 thf(decl_49, type, emptysetE: $o). 1.04/3.16 thf(decl_50, type, emptysetimpfalse: $o). 1.04/3.16 thf(decl_51, type, notinemptyset: $o). 1.04/3.16 thf(decl_52, type, exuE3e: $o). 1.04/3.16 thf(decl_53, type, setext: $o). 1.04/3.16 thf(decl_54, type, emptyI: $o). 1.04/3.16 thf(decl_55, type, noeltsimpempty: $o). 1.04/3.16 thf(decl_56, type, setbeta: $o). 1.04/3.16 thf(decl_57, type, nonempty: $i > $o). 1.04/3.16 thf(decl_58, type, nonemptyE1: $o). 1.04/3.16 thf(decl_59, type, nonemptyI: $o). 1.04/3.16 thf(decl_60, type, nonemptyI1: $o). 1.04/3.16 thf(decl_61, type, setadjoinIL: $o). 1.04/3.16 thf(decl_62, type, emptyinunitempty: $o). 1.04/3.16 thf(decl_63, type, setadjoinIR: $o). 1.04/3.16 thf(decl_64, type, setadjoinE: $o). 1.04/3.16 thf(decl_65, type, setadjoinOr: $o). 1.04/3.16 thf(decl_66, type, setoftrueEq: $o). 1.04/3.16 thf(decl_67, type, powersetI: $o). 1.04/3.16 thf(decl_68, type, emptyinPowerset: $o). 1.04/3.16 thf(decl_69, type, emptyInPowerset: $o). 1.04/3.16 thf(decl_70, type, powersetE: $o). 1.04/3.16 thf(decl_71, type, setunionI: $o). 1.04/3.16 thf(decl_72, type, setunionE: $o). 1.04/3.16 thf(decl_73, type, subPowSU: $o). 1.04/3.16 thf(decl_74, type, exuE2: $o). 1.04/3.16 thf(decl_75, type, nonemptyImpWitness: $o). 1.04/3.16 thf(decl_76, type, uniqinunit: $o). 1.04/3.16 thf(decl_77, type, notinsingleton: $o). 1.04/3.16 thf(decl_78, type, eqinunit: $o). 1.04/3.16 thf(decl_79, type, singletonsswitch: $o). 1.04/3.16 thf(decl_80, type, upairsetE: $o). 1.04/3.16 thf(decl_81, type, upairsetIL: $o). 1.04/3.16 thf(decl_82, type, upairsetIR: $o). 1.04/3.16 thf(decl_83, type, emptyE1: $o). 1.04/3.16 thf(decl_84, type, vacuousDall: $o). 1.04/3.16 thf(decl_85, type, quantDeMorgan1: $o). 1.04/3.16 thf(decl_86, type, quantDeMorgan2: $o). 1.04/3.16 thf(decl_87, type, quantDeMorgan3: $o). 1.04/3.16 thf(decl_88, type, quantDeMorgan4: $o). 1.04/3.16 thf(decl_89, type, prop2setI: $o). 1.04/3.16 thf(decl_90, type, set2prop: $i > $o). 1.04/3.16 thf(decl_91, type, prop2set2propI: $o). 1.04/3.16 thf(decl_92, type, notdexE: $o). 1.04/3.16 thf(decl_93, type, notdallE: $o). 1.04/3.16 thf(decl_94, type, exuI1: $o). 1.04/3.16 thf(decl_95, type, exuI3: $o). 1.04/3.16 thf(decl_96, type, exuI2: $o). 1.04/3.16 thf(decl_97, type, inCongP: $o). 1.04/3.16 thf(decl_98, type, in__Cong: $o). 1.04/3.16 thf(decl_99, type, exuE3u: $o). 1.04/3.16 thf(decl_100, type, exu__Cong: $o). 1.04/3.16 thf(decl_101, type, emptyset__Cong: $o). 1.04/3.16 thf(decl_102, type, setadjoin__Cong: $o). 1.04/3.16 thf(decl_103, type, powerset__Cong: $o). 1.04/3.16 thf(decl_104, type, setunion__Cong: $o). 1.04/3.16 thf(decl_105, type, omega__Cong: $o). 1.04/3.16 thf(decl_106, type, exuEu: $o). 1.04/3.16 thf(decl_107, type, descr__Cong: $o). 1.04/3.16 thf(decl_108, type, dsetconstr__Cong: $o). 1.04/3.16 thf(decl_109, type, subset: $i > $i > $o). 1.04/3.16 thf(decl_112, type, subsetI1: $o). 1.04/3.16 thf(decl_113, type, eqimpsubset2: $o). 1.04/3.16 thf(decl_114, type, eqimpsubset1: $o). 1.04/3.16 thf(decl_115, type, subsetI2: $o). 1.04/3.16 thf(decl_116, type, emptysetsubset: $o). 1.04/3.16 thf(decl_117, type, subsetE: $o). 1.04/3.16 thf(decl_118, type, subsetE2: $o). 1.04/3.16 thf(decl_119, type, notsubsetI: $o). 1.04/3.16 thf(decl_120, type, notequalI1: $o). 1.04/3.16 thf(decl_121, type, notequalI2: $o). 1.04/3.16 thf(decl_122, type, subsetRefl: $o). 1.04/3.16 thf(decl_123, type, subsetTrans: $o). 1.04/3.16 thf(decl_124, type, setadjoinSub: $o). 1.04/3.16 thf(decl_125, type, setadjoinSub2: $o). 1.04/3.16 thf(decl_126, type, subset2powerset: $o). 1.04/3.16 thf(decl_127, type, setextsub: $o). 1.04/3.16 thf(decl_128, type, subsetemptysetimpeq: $o). 1.04/3.16 thf(decl_129, type, powersetI1: $o). 1.04/3.16 thf(decl_130, type, powersetE1: $o). 1.04/3.16 thf(decl_131, type, inPowerset: $o). 1.04/3.16 thf(decl_132, type, powersetsubset: $o). 1.04/3.16 thf(decl_133, type, sepInPowerset: $o). 1.04/3.16 thf(decl_134, type, sepSubset: $o). 1.04/3.16 thf(decl_135, type, binunion: $i > $i > $i). 1.04/3.16 thf(decl_136, type, binunionIL: $o). 1.04/3.16 thf(decl_137, type, upairset2IR: $o). 1.04/3.16 thf(decl_138, type, binunionIR: $o). 1.04/3.16 thf(decl_139, type, binunionEcases: $o). 1.04/3.16 thf(decl_140, type, binunionE: $o). 1.04/3.16 thf(decl_141, type, binunionLsub: $o). 1.04/3.16 thf(decl_142, type, binunionRsub: $o). 1.04/3.16 thf(decl_143, type, binintersect: $i > $i > $i). 1.04/3.16 thf(decl_144, type, binintersectI: $o). 1.04/3.16 thf(decl_145, type, binintersectSubset5: $o). 1.04/3.16 thf(decl_146, type, binintersectEL: $o). 1.04/3.16 thf(decl_147, type, binintersectLsub: $o). 1.04/3.16 thf(decl_148, type, binintersectSubset2: $o). 1.04/3.16 thf(decl_149, type, binintersectSubset3: $o). 1.04/3.16 thf(decl_150, type, binintersectER: $o). 1.04/3.16 thf(decl_151, type, disjointsetsI1: $o). 1.04/3.16 thf(decl_152, type, binintersectRsub: $o). 1.04/3.16 thf(decl_153, type, binintersectSubset4: $o). 1.04/3.16 thf(decl_154, type, binintersectSubset1: $o). 1.04/3.16 thf(decl_155, type, bs114d: $o). 1.04/3.16 thf(decl_157, type, setminus: $i > $i > $i). 1.04/3.16 thf(decl_158, type, setminusI: $o). 1.04/3.16 thf(decl_159, type, setminusEL: $o). 1.04/3.16 thf(decl_160, type, setminusER: $o). 1.04/3.16 thf(decl_161, type, setminusSubset2: $o). 1.04/3.16 thf(decl_162, type, setminusERneg: $o). 1.04/3.16 thf(decl_163, type, setminusELneg: $o). 1.04/3.16 thf(decl_164, type, setminusILneg: $o). 1.04/3.16 thf(decl_165, type, setminusIRneg: $o). 1.04/3.16 thf(decl_166, type, setminusLsub: $o). 1.04/3.16 thf(decl_167, type, setminusSubset1: $o). 1.04/3.16 thf(decl_168, type, symdiff: $i > $i > $i). 1.04/3.16 thf(decl_169, type, symdiffE: $o). 1.04/3.16 thf(decl_170, type, symdiffI1: $o). 1.04/3.16 thf(decl_171, type, symdiffI2: $o). 1.04/3.16 thf(decl_172, type, symdiffIneg1: $o). 1.04/3.16 thf(decl_173, type, symdiffIneg2: $o). 1.04/3.16 thf(decl_174, type, iskpair: $i > $o). 1.04/3.16 thf(decl_175, type, secondinupair: $o). 1.04/3.16 thf(decl_176, type, setukpairIL: $o). 1.04/3.16 thf(decl_177, type, setukpairIR: $o). 1.04/3.16 thf(decl_178, type, kpairiskpair: $o). 1.04/3.16 thf(decl_179, type, kpair: $i > $i > $i). 1.04/3.16 thf(decl_180, type, kpairp: $o). 1.04/3.16 thf(decl_181, type, cartprod: $i > $i > $i). 1.04/3.16 thf(decl_182, type, singletonsubset: $o). 1.04/3.16 thf(decl_183, type, singletoninpowerset: $o). 1.04/3.16 thf(decl_184, type, singletoninpowunion: $o). 1.04/3.16 thf(decl_185, type, upairset2E: $o). 1.04/3.16 thf(decl_186, type, upairsubunion: $o). 1.04/3.16 thf(decl_187, type, upairinpowunion: $o). 1.04/3.16 thf(decl_188, type, ubforcartprodlem1: $o). 1.04/3.16 thf(decl_189, type, ubforcartprodlem2: $o). 1.04/3.16 thf(decl_190, type, ubforcartprodlem3: $o). 1.04/3.16 thf(decl_191, type, cartprodpairin: $o). 1.04/3.16 thf(decl_192, type, cartprodmempair1: $o). 1.04/3.16 thf(decl_193, type, cartprodmempair: $o). 1.04/3.16 thf(decl_194, type, setunionE2: $o). 1.04/3.16 thf(decl_195, type, setunionsingleton1: $o). 1.04/3.16 thf(decl_196, type, setunionsingleton2: $o). 1.04/3.16 thf(decl_197, type, setunionsingleton: $o). 1.04/3.16 thf(decl_198, type, singleton: $i > $o). 1.04/3.16 thf(decl_199, type, singletonprop: $o). 1.04/3.16 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 1.04/3.16 thf(decl_201, type, ex1E1: $o). 1.04/3.16 thf(decl_202, type, ex1I: $o). 1.04/3.16 thf(decl_203, type, ex1I2: $o). 1.04/3.16 thf(decl_204, type, singletonsuniq: $o). 1.04/3.16 thf(decl_209, type, setukpairinjL1: $o). 1.04/3.16 thf(decl_210, type, kfstsingleton: $o). 1.04/3.16 thf(decl_211, type, theprop: $o). 1.04/3.16 thf(decl_212, type, kfst: $i > $i). 1.04/3.16 thf(decl_213, type, kfstpairEq: $o). 1.04/3.16 thf(decl_214, type, cartprodfstin: $o). 1.04/3.16 thf(decl_215, type, setukpairinjL2: $o). 1.04/3.16 thf(decl_216, type, setukpairinjL: $o). 1.04/3.16 thf(decl_217, type, setukpairinjR11: $o). 1.04/3.16 thf(decl_218, type, setukpairinjR12: $o). 1.04/3.16 thf(decl_219, type, setukpairinjR1: $o). 1.04/3.16 thf(decl_220, type, upairequniteq: $o). 1.04/3.16 thf(decl_221, type, setukpairinjR2: $o). 1.04/3.16 thf(decl_222, type, setukpairinjR: $o). 1.04/3.16 thf(decl_223, type, ksndsingleton: $o). 1.04/3.16 thf(decl_224, type, ksnd: $i > $i). 1.04/3.16 thf(decl_225, type, ksndpairEq: $o). 1.04/3.16 thf(decl_226, type, kpairsurjEq: $o). 1.04/3.16 thf(decl_227, type, cartprodsndin: $o). 1.04/3.16 thf(decl_228, type, cartprodpairmemEL: $o). 1.04/3.16 thf(decl_229, type, cartprodpairmemER: $o). 1.04/3.16 thf(decl_230, type, cartprodmempaircEq: $o). 1.04/3.16 thf(decl_231, type, cartprodfstpairEq: $o). 1.04/3.16 thf(decl_232, type, cartprodsndpairEq: $o). 1.04/3.16 thf(decl_233, type, cartprodpairsurjEq: $o). 1.04/3.16 thf(decl_234, type, breln: $i > $i > $i > $o). 1.04/3.16 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 1.04/3.16 thf(decl_236, type, dpsetconstrI: $o). 1.04/3.16 thf(decl_237, type, dpsetconstrSub: $o). 1.04/3.16 thf(decl_238, type, setOfPairsIsBReln: $o). 1.04/3.16 thf(decl_239, type, dpsetconstrERa: $o). 1.04/3.16 thf(decl_240, type, dpsetconstrEL1: $o). 1.04/3.16 thf(decl_241, type, dpsetconstrEL2: $o). 1.04/3.16 thf(decl_242, type, dpsetconstrER: $o). 1.04/3.16 thf(decl_243, type, func: $i > $i > $i > $o). 1.04/3.16 thf(decl_244, type, funcSet: $i > $i > $i). 1.04/3.16 thf(decl_245, type, funcImageSingleton: $o). 1.04/3.16 thf(decl_246, type, apProp: $o). 1.04/3.16 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_248, type, app: $o). 1.04/3.16 thf(decl_249, type, infuncsetfunc: $o). 1.04/3.16 thf(decl_250, type, ap2p: $o). 1.04/3.16 thf(decl_251, type, funcinfuncset: $o). 1.04/3.16 thf(decl_252, type, lamProp: $o). 1.04/3.16 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 1.04/3.16 thf(decl_254, type, lamp: $o). 1.04/3.16 thf(decl_255, type, lam2p: $o). 1.04/3.16 thf(decl_256, type, brelnall1: $o). 1.04/3.16 thf(decl_257, type, brelnall2: $o). 1.04/3.16 thf(decl_258, type, ex1E2: $o). 1.04/3.16 thf(decl_259, type, funcGraphProp1: $o). 1.04/3.16 thf(decl_260, type, funcGraphProp3: $o). 1.04/3.16 thf(decl_261, type, funcGraphProp2: $o). 1.04/3.16 thf(decl_262, type, funcextLem: $o). 1.04/3.16 thf(decl_263, type, funcGraphProp4: $o). 1.04/3.16 thf(decl_264, type, subbreln: $o). 1.04/3.16 thf(decl_265, type, eqbreln: $o). 1.04/3.16 thf(decl_266, type, funcext: $o). 1.04/3.16 thf(decl_267, type, funcext2: $o). 1.04/3.16 thf(decl_268, type, ap2apEq1: $o). 1.04/3.16 thf(decl_269, type, ap2apEq2: $o). 1.04/3.16 thf(decl_270, type, beta1: $o). 1.04/3.16 thf(decl_271, type, eta1: $o). 1.04/3.16 thf(decl_272, type, lam2lamEq: $o). 1.04/3.16 thf(decl_273, type, beta2: $o). 1.04/3.16 thf(decl_274, type, eta2: $o). 1.04/3.16 thf(decl_275, type, epred1_0: $o). 1.04/3.16 thf(decl_276, type, esk1_2: $i > $i > $i). 1.04/3.16 thf(decl_277, type, esk2_2: $i > $i > $i). 1.04/3.16 thf(decl_278, type, esk3_2: $i > $i > $i). 1.04/3.16 thf(decl_279, type, esk4_1: $i > $i). 1.04/3.16 thf(decl_280, type, esk5_2: ($i > $i > $o) > $i > $i). 1.04/3.16 thf(decl_281, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 1.04/3.16 thf(decl_282, type, esk7_2: ($i > $i > $o) > $i > $i). 1.04/3.16 thf(decl_283, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 1.04/3.16 thf(decl_284, type, esk9_1: $i > $i). 1.04/3.16 thf(decl_285, type, esk10_2: ($i > $o) > $i > $i). 1.04/3.16 thf(decl_286, type, esk11_2: ($i > $o) > $i > $i). 1.04/3.16 thf(decl_287, type, esk12_1: ($i > $o) > $i). 1.04/3.16 thf(decl_288, type, esk13_2: ($i > $o) > $i > $i). 1.04/3.16 thf(decl_289, type, esk14_1: ($i > $o) > $i). 1.04/3.16 thf(decl_290, type, esk15_2: $i > $i > $i). 1.04/3.16 thf(decl_291, type, esk16_2: $i > $i > $i). 1.04/3.16 thf(decl_292, type, esk17_1: $i > $i). 1.04/3.16 thf(decl_293, type, esk18_1: $i > $i). 1.04/3.16 thf(decl_294, type, esk19_1: $i > $i). 1.04/3.16 thf(decl_295, type, esk20_2: $i > $i > $i). 1.04/3.16 thf(decl_296, type, esk21_3: $i > $i > $o > $i). 1.04/3.16 thf(decl_297, type, esk22_2: ($i > $o) > $i > $i). 1.04/3.16 thf(decl_298, type, esk23_1: ($i > $o) > $i). 1.04/3.16 thf(decl_299, type, esk24_1: $i > $i). 1.04/3.16 thf(decl_300, type, esk25_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_301, type, esk26_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_302, type, esk27_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_303, type, esk28_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_304, type, esk29_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_305, type, esk30_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_306, type, esk31_2: ($i > $o) > $i > $i). 1.04/3.16 thf(decl_307, type, esk32_1: ($i > $o) > $i). 1.04/3.16 thf(decl_308, type, esk33_1: ($i > $o) > $i). 1.04/3.16 thf(decl_309, type, esk34_1: ($i > $o) > $i). 1.04/3.16 thf(decl_310, type, esk35_1: ($i > $o) > $i). 1.04/3.16 thf(decl_311, type, esk36_2: ($i > $o) > $i > $i). 1.04/3.16 thf(decl_312, type, esk37_1: ($i > $o) > $i). 1.04/3.16 thf(decl_313, type, esk38_2: ($i > $o) > $i > $i). 1.04/3.16 thf(decl_314, type, esk39_2: ($i > $o) > ($i > $o) > $i). 1.04/3.16 thf(decl_315, type, esk40_2: ($i > $o) > ($i > $o) > $i). 1.04/3.16 thf(decl_316, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 1.04/3.16 thf(decl_317, type, esk42_2: ($i > $o) > ($i > $o) > $i). 1.04/3.16 thf(decl_318, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 1.04/3.16 thf(decl_319, type, esk44_2: ($i > $o) > ($i > $o) > $i). 1.04/3.16 thf(decl_320, type, esk45_2: ($i > $o) > $i > $i). 1.04/3.16 thf(decl_321, type, esk46_2: ($i > $o) > ($i > $o) > $i). 1.04/3.16 thf(decl_322, type, esk47_2: ($i > $o) > ($i > $o) > $i). 1.04/3.16 thf(decl_323, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 1.04/3.16 thf(decl_324, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 1.04/3.16 thf(decl_325, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1.04/3.16 thf(decl_326, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1.04/3.16 thf(decl_327, type, esk52_2: $i > $i > $i). 1.04/3.16 thf(decl_328, type, esk53_2: $i > $i > $i). 1.04/3.16 thf(decl_329, type, esk54_2: $i > $i > $i). 1.04/3.16 thf(decl_330, type, esk55_3: $i > $i > $i > $i). 1.04/3.16 thf(decl_331, type, esk56_3: $i > $i > $i > $i). 1.04/3.16 thf(decl_332, type, esk57_2: $i > $i > $i). 1.04/3.16 thf(decl_333, type, esk58_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_334, type, esk59_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_335, type, esk60_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_336, type, esk61_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_337, type, esk62_3: $i > ($i > $o) > $i > $i). 1.04/3.16 thf(decl_338, type, esk63_3: $i > ($i > $o) > $i > $i). 1.04/3.16 thf(decl_339, type, esk64_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_340, type, esk65_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_341, type, esk66_2: $i > ($i > $o) > $i). 1.04/3.16 thf(decl_342, type, esk67_1: $i > $i). 1.04/3.16 thf(decl_343, type, esk68_1: $i > $i). 1.04/3.16 thf(decl_344, type, esk69_4: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_345, type, esk70_3: $i > $i > ($i > $i) > $i). 1.04/3.16 thf(decl_346, type, esk71_3: $i > $i > ($i > $i) > $i). 1.04/3.16 thf(decl_347, type, esk72_3: $i > $i > ($i > $i) > $i). 1.04/3.16 thf(decl_348, type, esk73_4: $i > $i > $i > ($i > $o) > $i). 1.04/3.16 thf(decl_349, type, esk74_4: $i > $i > $i > ($i > $o) > $i). 1.04/3.16 thf(decl_350, type, esk75_4: $i > $i > $i > ($i > $o) > $i). 1.04/3.16 thf(decl_351, type, esk76_4: $i > $i > $i > ($i > $o) > $i). 1.04/3.16 thf(decl_352, type, esk77_4: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_353, type, esk78_4: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_354, type, esk79_4: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_355, type, esk80_4: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_356, type, esk81_4: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_357, type, esk82_4: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_358, type, esk83_4: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_359, type, esk84_4: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_360, type, esk85_4: $i > $i > $i > $i > $i). 1.04/3.16 thf(decl_361, type, esk86_3: $i > $i > ($i > $i) > $i). 1.04/3.16 thf(decl_362, type, esk87_3: $i > $i > ($i > $i) > $i). 1.04/3.16 thf(decl_363, type, esk88_3: $i > $i > ($i > $i) > $i). 1.04/3.16 thf(decl_364, type, esk89_0: $i). 1.04/3.16 thf(decl_365, type, epred2_0: $o). 1.04/3.16 thf(decl_366, type, esk90_0: $i). 1.04/3.16 thf(decl_367, type, esk91_0: $i). 1.04/3.16 thf(decl_373, type, epred3_0: $i > $o). 1.04/3.16 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ex1)). 1.04/3.16 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', singleton)). 1.04/3.16 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', replAx)). 1.04/3.16 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', exu)). 1.04/3.16 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', descrp)). 1.04/3.16 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', exuE1)). 1.04/3.16 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', exuE3e)). 1.04/3.16 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', nonempty)). 1.04/3.16 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', nonemptyI)). 1.04/3.16 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', exuE2)). 1.04/3.16 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', exuI1)). 1.04/3.16 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', exuI3)). 1.04/3.16 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', exuI2)). 1.04/3.16 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', exuE3u)). 1.04/3.16 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', exu__Cong)). 1.04/3.16 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', exuEu)). 1.04/3.16 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', descr__Cong)). 1.04/3.16 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', singletonprop)). 1.04/3.16 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ex1E1)). 1.04/3.16 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ex1I)). 1.04/3.16 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ex1I2)). 1.04/3.16 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', kfstsingleton)). 1.04/3.16 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ksndsingleton)). 1.04/3.16 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setOfPairsIsBReln)). 1.04/3.16 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', breln)). 1.04/3.16 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', funcImageSingleton)). 1.04/3.16 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ex1E2)). 1.04/3.16 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', dsetconstrI)). 1.04/3.16 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', dsetconstrEL)). 1.04/3.16 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', dsetconstrER)). 1.04/3.16 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setbeta)). 1.04/3.16 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', nonemptyE1)). 1.04/3.16 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', nonemptyI1)). 1.04/3.16 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setoftrueEq)). 1.04/3.16 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', nonemptyImpWitness)). 1.04/3.16 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', emptyE1)). 1.04/3.16 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', dsetconstr__Cong)). 1.04/3.16 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', sepInPowerset)). 1.04/3.16 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', sepSubset)). 1.04/3.16 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', theprop)). 1.04/3.16 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', dpsetconstrI)). 1.04/3.16 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', dpsetconstrSub)). 1.04/3.16 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', dpsetconstrERa)). 1.04/3.16 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', dpsetconstrEL1)). 1.04/3.16 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', dpsetconstrEL2)). 1.04/3.16 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', dpsetconstrER)). 1.04/3.16 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', apProp)). 1.04/3.16 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', lamProp)). 1.04/3.16 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', lamp)). 1.04/3.16 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', lam2p)). 1.04/3.16 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', brelnall1)). 1.04/3.16 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', brelnall2)). 1.04/3.16 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', subbreln)). 1.04/3.16 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', eqbreln)). 1.04/3.16 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', beta1)). 1.04/3.16 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', eta1)). 1.04/3.16 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', lam2lamEq)). 1.04/3.16 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', beta2)). 1.04/3.16 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', eta2)). 1.04/3.16 thf(iffalseProp1, conjecture, ((setextAx)=>((emptysetAx)=>((((setunionAx)=>(((((replAx)=>((foundationAx)=>(((descrp)=>((dsetconstrI)=>((((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>(((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((((setadjoinIR)=>((setadjoinE)=>(((setoftrueEq)=>((powersetI)=>(((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>(((((emptyE1)=>(((quantDeMorgan1)=>((((quantDeMorgan4)=>(((((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>(((exuE3u)=>(((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>(((exuEu)=>(((dsetconstr__Cong)=>((subsetI1)=>(((eqimpsubset1)=>((((((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>(((((setextsub)=>((subsetemptysetimpeq)=>(((powersetE1)=>((inPowerset)=>(((((binunionIL)=>(((binunionIR)=>((((binunionLsub)=>(((binintersectI)=>(((binintersectEL)=>(((binintersectSubset2)=>(((binintersectER)=>((((binintersectSubset4)=>(((((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>((((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>(((((kpairp)=>(((singletoninpowerset)=>((((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>(((setunionE2)=>(((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>(((ex1I)=>(((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>(((ksndpairEq)=>((kpairsurjEq)=>(((((cartprodmempaircEq)=>((((cartprodpairsurjEq)=>((((setOfPairsIsBReln)=>(((dpsetconstrEL1)=>((((funcImageSingleton)=>(((app)=>((infuncsetfunc)=>((ap2p)=>(((((lam2p)=>((brelnall1)=>((((funcGraphProp1)=>((funcGraphProp3)=>(((funcextLem)=>((((eqbreln)=>(((funcext2)=>(((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:(((((X14)=(X2))&(X39))|(((X14)=(X3))&~((X39)))))))))))))))))))<=(ap2apEq1)))<=(funcext)))<=(subbreln))<=(funcGraphProp4)))<=(funcGraphProp2))))<=(ex1E2))<=(brelnall2))))<=(lamp))<=(lamProp))<=(funcinfuncset)))))<=(apProp)))<=(dpsetconstrER))<=(dpsetconstrEL2)))<=(dpsetconstrERa)))<=(dpsetconstrSub))<=(dpsetconstrI)))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin))))<=(ksndsingleton)))))<=(setukpairinjR1))<=(setukpairinjR12)))))<=(cartprodfstin))<=(kfstpairEq))))))<=(ex1I2)))<=(ex1E1)))))<=(setunionsingleton1)))<=(cartprodmempair)))))))))<=(upairset2E))<=(singletoninpowunion)))<=(singletonsubset)))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))))))))<=(setminusSubset1))<=(setminusLsub))))<=(setminusELneg))))<=(setminusER)))<=(setminusI))<=(bs114d))<=(binintersectSubset1)))<=(binintersectRsub))<=(disjointsetsI1)))<=(binintersectSubset3)))<=(binintersectLsub)))<=(binintersectSubset5)))<=(binunionRsub)))<=(binunionE))<=(binunionEcases)))<=(upairset2IR)))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset))))<=(powersetI1))))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub)))))))<=(subsetE2))<=(subsetE))<=(emptysetsubset))<=(subsetI2)))<=(eqimpsubset2))))<=(descr__Cong)))<=(omega__Cong))))))<=(exu__Cong)))<=(in__Cong)))))))<=(notdexE))<=(prop2set2propI))<=(prop2setI)))<=(quantDeMorgan3))<=(quantDeMorgan2)))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))))<=(notinsingleton)))<=(nonemptyImpWitness))<=(exuE2)))))))<=(emptyinPowerset))))<=(setadjoinOr))))<=(emptyinunitempty))<=(setadjoinIL)))))))))<=(exuE3e)))))))<=(dsetconstrER))<=(dsetconstrEL))))<=(wellorderingAx))))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', iffalseProp1)). 1.04/3.16 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setextAx)). 1.04/3.16 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', emptysetAx)). 1.04/3.16 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setadjoinAx)). 1.04/3.16 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', powersetAx)). 1.04/3.16 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setunionAx)). 1.04/3.16 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', omega0Ax)). 1.04/3.16 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', omegaSAx)). 1.04/3.16 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', omegaIndAx)). 1.04/3.16 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', foundationAx)). 1.04/3.16 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', wellorderingAx)). 1.04/3.16 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', prop2setE)). 1.04/3.16 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', emptysetE)). 1.04/3.16 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', emptysetimpfalse)). 1.04/3.16 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', notinemptyset)). 1.04/3.16 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setext)). 1.04/3.16 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', emptyI)). 1.04/3.16 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', noeltsimpempty)). 1.04/3.16 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setadjoinIL)). 1.04/3.16 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', emptyinunitempty)). 1.04/3.16 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setadjoinIR)). 1.04/3.16 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setadjoinE)). 1.04/3.16 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setadjoinOr)). 1.04/3.16 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', powersetI)). 1.04/3.16 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', emptyinPowerset)). 1.04/3.16 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', emptyInPowerset)). 1.04/3.16 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', powersetE)). 1.04/3.16 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setunionI)). 1.04/3.16 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setunionE)). 1.04/3.16 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', subPowSU)). 1.04/3.16 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', uniqinunit)). 1.04/3.16 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', notinsingleton)). 1.04/3.16 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', eqinunit)). 1.04/3.16 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', singletonsswitch)). 1.04/3.16 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', upairsetE)). 1.04/3.16 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', upairsetIL)). 1.04/3.16 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', upairsetIR)). 1.04/3.16 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', vacuousDall)). 1.04/3.16 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', quantDeMorgan1)). 1.04/3.16 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', quantDeMorgan2)). 1.04/3.16 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', quantDeMorgan3)). 1.04/3.16 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', quantDeMorgan4)). 1.04/3.16 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', prop2setI)). 1.04/3.16 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', prop2set2propI)). 1.04/3.16 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', notdexE)). 1.04/3.16 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', notdallE)). 1.04/3.16 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', inCongP)). 1.04/3.16 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', in__Cong)). 1.04/3.16 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', emptyset__Cong)). 1.04/3.16 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setadjoin__Cong)). 1.04/3.16 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', powerset__Cong)). 1.04/3.16 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setunion__Cong)). 1.04/3.16 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', omega__Cong)). 1.04/3.16 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', subsetI1)). 1.04/3.16 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', eqimpsubset2)). 1.04/3.16 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', eqimpsubset1)). 1.04/3.16 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', subsetI2)). 1.04/3.16 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', emptysetsubset)). 1.04/3.16 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', subsetE)). 1.04/3.16 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', subsetE2)). 1.04/3.16 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', notsubsetI)). 1.04/3.16 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', notequalI1)). 1.04/3.16 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', notequalI2)). 1.04/3.16 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', subsetRefl)). 1.04/3.16 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', subsetTrans)). 1.04/3.16 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setadjoinSub)). 1.04/3.16 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setadjoinSub2)). 1.04/3.16 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', subset2powerset)). 1.04/3.16 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setextsub)). 1.04/3.16 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', subsetemptysetimpeq)). 1.04/3.16 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', powersetI1)). 1.04/3.16 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', powersetE1)). 1.04/3.16 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', inPowerset)). 1.04/3.16 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', powersetsubset)). 1.04/3.16 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binunionIL)). 1.04/3.16 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', upairset2IR)). 1.04/3.16 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binunionIR)). 1.04/3.16 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binunionEcases)). 1.04/3.16 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binunionE)). 1.04/3.16 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binunionLsub)). 1.04/3.16 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binunionRsub)). 1.04/3.16 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binintersectI)). 1.04/3.16 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binintersectSubset5)). 1.04/3.16 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binintersectEL)). 1.04/3.16 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binintersectLsub)). 1.04/3.16 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binintersectSubset2)). 1.04/3.16 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binintersectSubset3)). 1.04/3.16 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binintersectER)). 1.04/3.16 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', disjointsetsI1)). 1.04/3.16 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binintersectRsub)). 1.04/3.16 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binintersectSubset4)). 1.04/3.16 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', binintersectSubset1)). 1.04/3.16 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', bs114d)). 1.04/3.16 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setminusI)). 1.04/3.16 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setminusEL)). 1.04/3.16 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setminusER)). 1.04/3.16 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setminusSubset2)). 1.04/3.16 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setminusERneg)). 1.04/3.16 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setminusELneg)). 1.04/3.16 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setminusILneg)). 1.04/3.16 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setminusIRneg)). 1.04/3.16 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setminusLsub)). 1.04/3.16 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setminusSubset1)). 1.04/3.16 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', symdiffE)). 1.04/3.16 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', symdiffI1)). 1.04/3.16 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', symdiffI2)). 1.04/3.16 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', symdiffIneg1)). 1.04/3.16 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', symdiffIneg2)). 1.04/3.16 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', secondinupair)). 1.04/3.16 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setukpairIL)). 1.04/3.16 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setukpairIR)). 1.04/3.16 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', kpairiskpair)). 1.04/3.16 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', kpairp)). 1.04/3.16 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', singletonsubset)). 1.04/3.16 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', singletoninpowerset)). 1.04/3.16 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', singletoninpowunion)). 1.04/3.16 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', upairset2E)). 1.04/3.16 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', upairsubunion)). 1.04/3.16 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', upairinpowunion)). 1.04/3.16 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ubforcartprodlem1)). 1.04/3.16 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ubforcartprodlem2)). 1.04/3.16 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ubforcartprodlem3)). 1.04/3.16 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodpairin)). 1.04/3.16 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodmempair1)). 1.04/3.16 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodmempair)). 1.04/3.16 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setunionE2)). 1.04/3.16 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setunionsingleton1)). 1.04/3.16 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setunionsingleton2)). 1.04/3.16 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setunionsingleton)). 1.04/3.16 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', singletonsuniq)). 1.04/3.16 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setukpairinjL1)). 1.04/3.16 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', kfstpairEq)). 1.04/3.16 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodfstin)). 1.04/3.16 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setukpairinjL2)). 1.04/3.16 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setukpairinjL)). 1.04/3.16 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setukpairinjR11)). 1.04/3.16 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setukpairinjR12)). 1.04/3.16 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setukpairinjR1)). 1.04/3.17 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', upairequniteq)). 1.04/3.17 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setukpairinjR2)). 1.04/3.17 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', setukpairinjR)). 1.04/3.17 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ksndpairEq)). 1.04/3.17 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', kpairsurjEq)). 1.04/3.17 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodsndin)). 1.04/3.17 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodpairmemEL)). 1.04/3.17 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodpairmemER)). 1.04/3.17 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodmempaircEq)). 1.04/3.17 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodfstpairEq)). 1.04/3.17 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodsndpairEq)). 1.04/3.17 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', cartprodpairsurjEq)). 1.04/3.17 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', app)). 1.04/3.17 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', infuncsetfunc)). 1.04/3.17 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ap2p)). 1.04/3.17 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', funcinfuncset)). 1.04/3.17 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', funcGraphProp1)). 1.04/3.17 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', funcGraphProp3)). 1.04/3.17 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', funcGraphProp2)). 1.04/3.17 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', funcextLem)). 1.04/3.17 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', funcGraphProp4)). 1.04/3.17 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', funcext)). 1.04/3.17 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', funcext2)). 1.04/3.17 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ap2apEq1)). 1.04/3.17 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3upwwCJ3LD/E---3.1_14603.p', ap2apEq2)). 1.04/3.17 thf(c_0_222, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X731:$i]:(((in @ X731 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X731 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])). 1.04/3.17 thf(c_0_223, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])). 1.04/3.17 thf(c_0_224, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 1.04/3.17 thf(c_0_225, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 1.04/3.17 thf(c_0_226, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 1.04/3.17 thf(c_0_227, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 1.04/3.17 thf(c_0_228, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 1.04/3.17 thf(c_0_229, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 1.04/3.17 thf(c_0_230, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 1.04/3.17 thf(c_0_231, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 1.04/3.17 thf(c_0_232, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 1.04/3.17 thf(c_0_233, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 1.04/3.17 thf(c_0_234, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 1.04/3.17 thf(c_0_235, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 1.04/3.17 thf(c_0_236, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 1.04/3.17 thf(c_0_237, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 1.04/3.17 thf(c_0_238, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 1.04/3.17 thf(c_0_239, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 1.04/3.17 thf(c_0_240, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 1.04/3.17 thf(c_0_241, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X731:$i]:(((in @ X731 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X731 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_222, c_0_223])). 1.04/3.17 thf(c_0_242, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 1.04/3.17 thf(c_0_243, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 1.04/3.17 thf(c_0_244, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 1.04/3.17 thf(c_0_245, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 1.04/3.17 thf(c_0_246, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 1.04/3.17 thf(c_0_247, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 1.04/3.17 thf(c_0_248, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 1.04/3.17 thf(c_0_249, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 1.04/3.17 thf(c_0_250, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X702:$i]:((((X6 @ X2 @ X702))&![X703:$i]:((((X6 @ X2 @ X703))=>((X702)=(X703)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_224, c_0_225])). 1.04/3.17 thf(c_0_251, plain, ((descrp)=(![X1:$i > $o]:(((?[X704:$i]:((((X1 @ X704))&![X705:$i]:((((X1 @ X705))=>((X704)=(X705)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_225])). 1.04/3.17 thf(c_0_252, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 1.04/3.17 thf(c_0_253, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 1.04/3.17 thf(c_0_254, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 1.04/3.17 thf(c_0_255, plain, ((exuE1)=(![X1:$i > $o]:(((?[X706:$i]:((((X1 @ X706))&![X707:$i]:((((X1 @ X707))=>((X706)=(X707)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_225])). 1.04/3.17 thf(c_0_256, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X708:$i]:((((X1 @ X708))&![X709:$i]:((((X1 @ X709))=>((X708)=(X709)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_228, c_0_225])). 1.04/3.17 thf(c_0_257, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 1.04/3.17 thf(c_0_258, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_229])). 1.04/3.17 thf(c_0_259, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_229])). 1.04/3.17 thf(c_0_260, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_229])). 1.04/3.17 thf(c_0_261, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 1.04/3.17 thf(c_0_262, plain, ((exuE2)=(![X1:$i > $o]:(((?[X710:$i]:((((X1 @ X710))&![X711:$i]:((((X1 @ X711))=>((X710)=(X711)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_231, c_0_225])). 1.04/3.17 thf(c_0_263, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_229])). 1.04/3.17 thf(c_0_264, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 1.04/3.17 thf(c_0_265, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X712:$i]:((((X1 @ X712))&![X713:$i]:((((X1 @ X713))=>((X712)=(X713))))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_225])). 1.04/3.17 thf(c_0_266, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X714:$i]:((((X1 @ X714))&![X715:$i]:((((X1 @ X715))=>((X714)=(X715)))))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_225])). 1.04/3.17 thf(c_0_267, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X716:$i]:((((X1 @ X716))&![X717:$i]:((((X1 @ X717))=>((X716)=(X717))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_225])). 1.04/3.17 thf(c_0_268, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X718:$i]:((((X1 @ X718))&![X719:$i]:((((X1 @ X719))=>((X718)=(X719)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_235, c_0_225])). 1.04/3.17 thf(c_0_269, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X720:$i]:((((X1 @ X720))&![X721:$i]:((((X1 @ X721))=>((X720)=(X721)))))))<=>(?[X722:$i]:((((X17 @ X722))&![X723:$i]:((((X17 @ X723))=>((X722)=(X723)))))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_225])). 1.04/3.17 thf(c_0_270, plain, ((exuEu)=(![X1:$i > $o]:(((?[X724:$i]:((((X1 @ X724))&![X725:$i]:((((X1 @ X725))=>((X724)=(X725)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_225])). 1.04/3.17 thf(c_0_271, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X726:$i]:((((X1 @ X726))&![X727:$i]:((((X1 @ X727))=>((X726)=(X727)))))))=>((?[X728:$i]:((((X17 @ X728))&![X729:$i]:((((X17 @ X729))=>((X728)=(X729)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_225])). 1.04/3.17 thf(c_0_272, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 1.04/3.17 thf(c_0_273, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 1.04/3.17 thf(c_0_274, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 1.04/3.17 thf(c_0_275, plain, ((singletonprop)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(?[X730:$i]:(((in @ X730 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X730 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_223])). 1.04/3.17 thf(c_0_276, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X732:$i]:(((in @ X732 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X732 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_241])). 1.04/3.17 thf(c_0_277, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X733:$i]:(((in @ X733 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X733 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_241])). 1.04/3.17 thf(c_0_278, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(?[X734:$i]:(((in @ X734 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X734 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_241])). 1.04/3.17 thf(c_0_279, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X735:$i]:(((in @ X735 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X735 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_223])). 1.04/3.17 thf(c_0_280, axiom, ((theprop)=(![X21:$i]:(((?[X736:$i]:(((in @ X736 @ X21)&((X21)=(setadjoin @ X736 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_223])). 1.04/3.17 thf(c_0_281, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X737:$i]:(((in @ X737 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X737 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_223])). 1.04/3.17 thf(c_0_282, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 1.04/3.17 thf(c_0_283, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 1.04/3.17 thf(c_0_284, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_246, c_0_247])). 1.04/3.17 thf(c_0_285, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 1.04/3.17 thf(c_0_286, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 1.04/3.17 thf(c_0_287, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 1.04/3.17 thf(c_0_288, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 1.04/3.17 thf(c_0_289, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(?[X738:$i]:(((in @ X738 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X738 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_248, c_0_223])). 1.04/3.17 thf(c_0_290, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 1.04/3.17 thf(c_0_291, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 1.04/3.17 thf(c_0_292, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 1.04/3.17 thf(c_0_293, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 1.04/3.17 thf(c_0_294, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_247])). 1.04/3.17 thf(c_0_295, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_247])). 1.04/3.17 thf(c_0_296, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((?[X739:$i]:(((in @ X739 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X739 @ emptyset)))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_241])). 1.04/3.17 thf(c_0_297, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_247])). 1.04/3.17 thf(c_0_298, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_247])). 1.04/3.17 thf(c_0_299, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 1.04/3.17 thf(c_0_300, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 1.04/3.17 thf(c_0_301, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 1.04/3.17 thf(c_0_302, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 1.04/3.17 thf(c_0_303, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 1.04/3.17 thf(c_0_304, plain, ((epred1_0)<=>![X1406:$i]:(?[X1407:$i]:((((![X1408:$i]:(((in @ X1408 @ X1407)=>![X1409:$i]:(((in @ X1409 @ X1408)=>(in @ X1409 @ X1406)))))&![X1410:$i, X1411:$i]:((((in @ X1410 @ X1406)&(in @ X1411 @ X1406))=>(![X1412:$i]:(((in @ X1412 @ X1407)=>((in @ X1410 @ X1412)<=>(in @ X1411 @ X1412))))=>((X1410)=(X1411))))))&![X1413:$i, X1414:$i]:((((in @ X1413 @ X1407)&(in @ X1414 @ X1407))=>(![X1415:$i]:(((in @ X1415 @ X1413)=>(in @ X1415 @ X1414)))|![X1416:$i]:(((in @ X1416 @ X1414)=>(in @ X1416 @ X1413)))))))&![X1417:$i]:(((![X1418:$i]:(((in @ X1418 @ X1417)=>(in @ X1418 @ X1406)))&?[X1419:$i]:((in @ X1419 @ X1417)))=>?[X1420:$i, X1421:$i]:(((((in @ X1420 @ X1407)&(in @ X1421 @ X1417))&~(?[X1422:$i]:(((in @ X1422 @ X1420)&(in @ X1422 @ X1417)))))&![X1423:$i]:(((in @ X1423 @ X1407)=>(![X1424:$i]:(((in @ X1424 @ X1423)=>(in @ X1424 @ X1420)))|(in @ X1421 @ X1423)))))))))))), introduced(definition)). 1.04/3.17 thf(c_0_305, negated_conjecture, ~((![X740:$i, X741:$i]:((![X742:$i]:(((in @ X742 @ X740)<=>(in @ X742 @ X741)))=>((X740)=(X741))))=>(![X743:$i]:(~(in @ X743 @ emptyset))=>(![X1432:$i, X1433:$i, X1434:$i]:(((in @ X1434 @ (setadjoin @ X1432 @ X1433))<=>(((X1434)=(X1432))|(in @ X1434 @ X1433))))=>(![X1429:$i, X1430:$i]:(((in @ X1430 @ (powerset @ X1429))<=>![X1431:$i]:(((in @ X1431 @ X1430)=>(in @ X1431 @ X1429)))))=>(![X744:$i, X745:$i]:(((in @ X745 @ (setunion @ X744))<=>?[X746:$i]:(((in @ X745 @ X746)&(in @ X746 @ X744)))))=>((in @ emptyset @ omega)=>(![X1428:$i]:(((in @ X1428 @ omega)=>(in @ (setadjoin @ X1428 @ X1428) @ omega)))=>(![X1425:$i]:((((in @ emptyset @ X1425)&![X1426:$i]:((((in @ X1426 @ omega)&(in @ X1426 @ X1425))=>(in @ (setadjoin @ X1426 @ X1426) @ X1425))))=>![X1427:$i]:(((in @ X1427 @ omega)=>(in @ X1427 @ X1425)))))=>(![X747:$i > $i > $o, X748:$i]:((![X749:$i]:(((in @ X749 @ X748)=>?[X750:$i]:(((X747 @ X749 @ X750)&![X751:$i]:(((X747 @ X749 @ X751)=>((X750)=(X751))))))))=>?[X752:$i]:(![X753:$i]:(((in @ X753 @ X752)<=>?[X754:$i]:(((in @ X754 @ X748)&(X747 @ X754 @ X753))))))))=>(![X755:$i]:((?[X756:$i]:((in @ X756 @ X755))=>?[X757:$i]:(((in @ X757 @ X755)&~(?[X758:$i]:(((in @ X758 @ X757)&(in @ X758 @ X755))))))))=>((epred1_0)=>(![X759:$i > $o]:((?[X760:$i]:(((X759 @ X760)&![X761:$i]:(((X759 @ X761)=>((X760)=(X761))))))=>(X759 @ (descr @ (^[Z0/* 17 */:$i]:(X759 @ Z0))))))=>(![X762:$i, X763:$i > $o, X764:$i]:(((in @ X764 @ X762)=>((X763 @ X764)=>(in @ X764 @ (dsetconstr @ X762 @ X763)))))=>(![X1403:$i, X1404:$i > $o, X1405:$i]:(((in @ X1405 @ (dsetconstr @ X1403 @ X1404))=>(in @ X1405 @ X1403)))=>(![X1400:$i, X1401:$i > $o, X1402:$i]:(((in @ X1402 @ (dsetconstr @ X1400 @ X1401))=>(X1401 @ X1402)))=>(![X765:$i > $o]:((?[X766:$i]:(((X765 @ X766)&![X767:$i]:(((X765 @ X767)=>((X766)=(X767))))))=>?[X768:$i]:(((X765 @ X768)&![X769:$i]:(((X765 @ X769)=>((X768)=(X769))))))))=>(![X770:$o, X771:$i]:(((in @ X771 @ (prop2set @ ((X770))))=>(X770)))=>(![X772:$i]:(((in @ X772 @ emptyset)=>![X773:$o]:((X773))))=>(![X774:$i]:(((in @ X774 @ emptyset)=>~($true)))=>(![X775:$i]:(~(in @ X775 @ emptyset))=>(![X1396:$i > $o]:((?[X1397:$i]:(((X1396 @ X1397)&![X1398:$i]:(((X1396 @ X1398)=>((X1397)=(X1398))))))=>?[X1399:$i]:((X1396 @ X1399))))=>(![X776:$i, X777:$i]:((![X778:$i]:(((in @ X778 @ X776)=>(in @ X778 @ X777)))=>(![X779:$i]:(((in @ X779 @ X777)=>(in @ X779 @ X776)))=>((X776)=(X777)))))=>(![X780:$i]:((![X781:$i]:(~(in @ X781 @ X780))=>((X780)=(emptyset))))=>(![X782:$i]:((![X783:$i]:(~(in @ X783 @ X782))=>((X782)=(emptyset))))=>(![X784:$i, X785:$i > $o, X786:$i]:(((in @ X786 @ X784)=>((in @ X786 @ (dsetconstr @ X784 @ X785))<=>(X785 @ X786))))=>(![X787:$i]:((((X787)!=(emptyset))=>?[X788:$i]:((in @ X788 @ X787))))=>(![X789:$i, X790:$i > $o, X791:$i]:(((in @ X791 @ X789)=>((X790 @ X791)=>((dsetconstr @ X789 @ X790)!=(emptyset)))))=>(![X792:$i]:((?[X793:$i]:((in @ X793 @ X792))=>((X792)!=(emptyset))))=>(![X1394:$i, X1395:$i]:((in @ X1394 @ (setadjoin @ X1394 @ X1395)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X794:$i, X795:$i, X796:$i]:(((in @ X796 @ X795)=>(in @ X796 @ (setadjoin @ X794 @ X795))))=>(![X797:$i, X798:$i, X799:$i]:(((in @ X799 @ (setadjoin @ X797 @ X798))=>![X800:$o]:(((((X799)=(X797))=>(X800))=>(((in @ X799 @ X798)=>(X800))=>(X800))))))=>(![X1391:$i, X1392:$i, X1393:$i]:(((in @ X1393 @ (setadjoin @ X1391 @ X1392))=>(((X1393)=(X1391))|(in @ X1393 @ X1392))))=>(![X801:$i]:(((dsetconstr @ X801 @ (^[Z0/* 1 */:$i]:($true)))=(X801)))=>(![X802:$i, X803:$i]:((![X804:$i]:(((in @ X804 @ X803)=>(in @ X804 @ X802)))=>(in @ X803 @ (powerset @ X802))))=>(![X1390:$i]:((in @ emptyset @ (powerset @ X1390)))=>(![X805:$i]:((in @ emptyset @ (powerset @ X805)))=>(![X806:$i, X807:$i, X808:$i]:(((in @ X807 @ (powerset @ X806))=>((in @ X808 @ X807)=>(in @ X808 @ X806))))=>(![X809:$i, X810:$i, X811:$i]:(((in @ X810 @ X811)=>((in @ X811 @ X809)=>(in @ X810 @ (setunion @ X809)))))=>(![X812:$i, X813:$i]:(((in @ X813 @ (setunion @ X812))=>![X814:$o]:((![X815:$i]:(((in @ X813 @ X815)=>((in @ X815 @ X812)=>(X814))))=>(X814)))))=>(![X816:$i, X817:$i]:(((in @ X817 @ X816)=>(in @ X817 @ (powerset @ (setunion @ X816)))))=>(![X1385:$i > $o]:((?[X1386:$i]:(((X1385 @ X1386)&![X1387:$i]:(((X1385 @ X1387)=>((X1386)=(X1387))))))=>?[X1388:$i]:(![X1389:$i]:(((X1385 @ X1389)<=>((X1389)=(X1388)))))))=>(![X1383:$i]:((((X1383)!=(emptyset))=>?[X1384:$i]:(((in @ X1384 @ X1383)&$true))))=>(![X818:$i, X819:$i]:(((in @ X818 @ (setadjoin @ X819 @ emptyset))=>((X818)=(X819))))=>(![X1381:$i, X1382:$i]:((((X1381)!=(X1382))=>~(in @ X1382 @ (setadjoin @ X1381 @ emptyset))))=>(![X820:$i, X821:$i]:((((X820)=(X821))=>(in @ X820 @ (setadjoin @ X821 @ emptyset))))=>(![X822:$i, X823:$i]:(((in @ X822 @ (setadjoin @ X823 @ emptyset))=>(in @ X823 @ (setadjoin @ X822 @ emptyset))))=>(![X1378:$i, X1379:$i, X1380:$i]:(((in @ X1380 @ (setadjoin @ X1378 @ (setadjoin @ X1379 @ emptyset)))=>(((X1380)=(X1378))|((X1380)=(X1379)))))=>(![X1376:$i, X1377:$i]:((in @ X1376 @ (setadjoin @ X1376 @ (setadjoin @ X1377 @ emptyset))))=>(![X1374:$i, X1375:$i]:((in @ X1375 @ (setadjoin @ X1374 @ (setadjoin @ X1375 @ emptyset))))=>(![X824:$i, X825:$i > $o]:((?[X826:$i]:(((in @ X826 @ X824)&(X825 @ X826)))=>(((dsetconstr @ X824 @ X825)=(emptyset))=>~($true))))=>(![X1372:$i > $o, X1373:$i]:(((in @ X1373 @ emptyset)=>(X1372 @ X1373)))=>(![X827:$i, X828:$i > $o]:((~(![X829:$i]:(((in @ X829 @ X827)=>(X828 @ X829))))=>?[X830:$i]:(((in @ X830 @ X827)&~((X828 @ X830))))))=>(![X1368:$i, X1369:$i > $o]:((![X1370:$i]:(((in @ X1370 @ X1368)=>~((X1369 @ X1370))))=>~(?[X1371:$i]:(((in @ X1371 @ X1368)&(X1369 @ X1371))))))=>(![X1364:$i, X1365:$i > $o]:((~(?[X1366:$i]:(((in @ X1366 @ X1364)&(X1365 @ X1366))))=>![X1367:$i]:(((in @ X1367 @ X1364)=>~((X1365 @ X1367))))))=>(![X831:$i, X832:$i > $o]:((?[X833:$i]:(((in @ X833 @ X831)&~((X832 @ X833))))=>~(![X834:$i]:(((in @ X834 @ X831)=>(X832 @ X834))))))=>(![X1363:$o]:(((X1363)=>(in @ emptyset @ (prop2set @ ((X1363))))))=>(![X1362:$o]:(((X1362)=>(set2prop @ (prop2set @ ((X1362))))))=>(![X1358:$i, X1359:$i > $o]:((~(?[X1360:$i]:(((in @ X1360 @ X1358)&(X1359 @ X1360))))=>![X1361:$i]:(((in @ X1361 @ X1358)=>~((X1359 @ X1361))))))=>(![X835:$i, X836:$i > $o]:((~(![X837:$i]:(((in @ X837 @ X835)=>(X836 @ X837))))=>?[X838:$i]:(((in @ X838 @ X835)&~((X836 @ X838))))))=>(![X839:$i > $o]:((?[X840:$i]:(((X839 @ X840)&![X841:$i]:(((X839 @ X841)=>((X840)=(X841))))))=>?[X842:$i]:(((X839 @ X842)&![X843:$i]:(((X839 @ X843)=>((X842)=(X843))))))))=>(![X844:$i > $o]:((?[X845:$i]:((X844 @ X845))=>(![X846:$i, X847:$i]:(((X844 @ X846)=>((X844 @ X847)=>((X846)=(X847)))))=>?[X848:$i]:(((X844 @ X848)&![X849:$i]:(((X844 @ X849)=>((X848)=(X849)))))))))=>(![X850:$i > $o]:((?[X851:$i]:(![X852:$i]:(((X850 @ X852)<=>((X852)=(X851)))))=>?[X853:$i]:(((X850 @ X853)&![X854:$i]:(((X850 @ X854)=>((X853)=(X854))))))))=>(![X855:$i, X856:$i]:((((X855)=(X856))=>![X857:$i, X858:$i]:((((X857)=(X858))=>((in @ X857 @ X855)=>(in @ X858 @ X856))))))=>(![X1354:$i, X1355:$i]:((((X1354)=(X1355))=>![X1356:$i, X1357:$i]:((((X1356)=(X1357))=>((in @ X1356 @ X1354)<=>(in @ X1357 @ X1355))))))=>(![X859:$i > $o]:((?[X860:$i]:(((X859 @ X860)&![X861:$i]:(((X859 @ X861)=>((X860)=(X861))))))=>![X862:$i, X863:$i]:(((X859 @ X862)=>((X859 @ X863)=>((X862)=(X863)))))))=>(![X1346:$i > $o, X1347:$i > $o]:((![X1348:$i, X1349:$i]:((((X1348)=(X1349))=>((X1346 @ X1348)<=>(X1347 @ X1349))))=>(?[X1350:$i]:(((X1346 @ X1350)&![X1351:$i]:(((X1346 @ X1351)=>((X1350)=(X1351))))))<=>?[X1352:$i]:(((X1347 @ X1352)&![X1353:$i]:(((X1347 @ X1353)=>((X1352)=(X1353)))))))))=>(((emptyset)=(emptyset))=>(![X864:$i, X865:$i]:((((X864)=(X865))=>![X866:$i, 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c_0_270]), c_0_271]), c_0_272]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_273]), c_0_274]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_275]), c_0_276]), c_0_277]), c_0_278]), singletonsuniq]), setukpairinjL1]), c_0_279]), c_0_280]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_281]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_282]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_297]), c_0_298]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_299]), c_0_300]), c_0_301]), c_0_302]), c_0_303])])]), c_0_304])). 1.04/3.17 thf(c_0_306, negated_conjecture, ![X1435:$i, X1436:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1448:$i, X1449:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1457:$i, X1458:$i > $i > $o, X1459:$i, X1461:$i, X1464:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1471:$i, X1472:$i > $o, X1473:$i, X1475:$i, X1476:$i > $o, X1477:$i, X1478:$i, X1479:$i > $o, X1480:$i, X1481:$i, X1482:$i > $o, X1483:$i, X1484:$i > $o, X1485:$i, X1488:$i, X1489:$o, X1490:$i, X1491:$i, X1492:$o, X1493:$i, X1494:$i, X1495:$i > $o, X1496:$i, X1499:$i, X1500:$i, X1503:$i, X1505:$i, X1507:$i, X1508:$i > $o, X1509:$i, X1510:$i, X1512:$i, X1513:$i > $o, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$o, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$o, X1545:$i, X1546:$i, X1547:$i > $o, X1548:$i, X1551:$i, X1552:$i, X1553:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i > $o, X1572:$i, X1573:$i > $o, X1574:$i, X1575:$i, X1576:$i > $o, X1577:$i, X1579:$i, X1580:$i > $o, X1582:$i, X1583:$i, X1584:$i > $o, X1586:$i, X1587:$i, X1588:$i > $o, X1589:$i, X1591:$o, X1592:$o, X1593:$i, X1594:$i > $o, X1596:$i, X1597:$i, X1598:$i > $o, X1599:$i, X1601:$i > $o, X1602:$i, X1605:$i, X1606:$i > $o, X1607:$i, X1611:$i, X1612:$i > $o, X1613:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i > $o, X1626:$i, X1628:$i, X1629:$i, X1630:$i > $o, X1631:$i > $o, X1634:$i, X1637:$i, X1638:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i > $o, X1651:$i, X1653:$i, X1654:$i, X1655:$i > $o, X1656:$i > $o, X1659:$i, X1661:$i, X1663:$i, X1664:$i, X1665:$i > $o, X1666:$i > $o, X1669:$i, X1670:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i > $o, X1717:$i, X1718:$i > $o, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$o, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$o, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i > $o, X1873:$i, X1875:$i, X1876:$i > $o, X1877:$i, X1879:$i, X1880:$i > $o, X1881:$i, X1884:$i, X1885:$i > $o, X1888:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i > $i > $o, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i > $i > $o, X1970:$i, X1971:$i, X1972:$i > $i > $o, X1973:$i, X1974:$i, X1975:$i > $i > $o, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i > $i > $o, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i > $i > $o, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i > $i > $o, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i > $i, X2020:$i, X2021:$i, X2022:$i > $i, X2024:$i, X2025:$i, X2026:$i > $i, X2028:$i, X2029:$i, X2030:$i, X2031:$i > $o, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i > $o, X2041:$i, X2042:$i, X2043:$i > $o, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i > $i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i > $i, X2116:$i, X2117:$i, X2118:$i > $i, X2120:$i, X2121:$i, X2122:$i, X2123:$i]:((((~(in @ (esk1_2 @ X1435 @ X1436) @ X1435)|~(in @ (esk1_2 @ X1435 @ X1436) @ X1436)|((X1435)=(X1436)))&((in @ (esk1_2 @ X1435 @ X1436) @ X1435)|(in @ (esk1_2 @ X1435 @ X1436) @ X1436)|((X1435)=(X1436))))&(~(in @ X1438 @ emptyset)&(((~(in @ X1441 @ (setadjoin @ X1439 @ X1440))|(((X1441)=(X1439))|(in @ X1441 @ X1440)))&((((X1441)!=(X1439))|(in @ X1441 @ (setadjoin @ X1439 @ X1440)))&(~(in @ X1441 @ X1440)|(in @ X1441 @ (setadjoin @ X1439 @ X1440)))))&(((~(in @ X1443 @ (powerset @ X1442))|(~(in @ X1444 @ X1443)|(in @ X1444 @ X1442)))&(((in @ (esk2_2 @ X1445 @ X1446) @ X1446)|(in @ X1446 @ (powerset @ X1445)))&(~(in @ (esk2_2 @ X1445 @ X1446) @ X1445)|(in @ X1446 @ (powerset @ X1445)))))&(((((in @ X1449 @ (esk3_2 @ X1448 @ X1449))|~(in @ X1449 @ (setunion @ X1448)))&((in @ (esk3_2 @ X1448 @ X1449) @ X1448)|~(in @ X1449 @ (setunion @ X1448))))&(~(in @ X1452 @ X1453)|~(in @ X1453 @ X1451)|(in @ X1452 @ (setunion @ X1451))))&((in @ emptyset @ omega)&((~(in @ X1454 @ omega)|(in @ (setadjoin @ X1454 @ X1454) @ omega))&(((((in @ (esk4_1 @ X1455) @ omega)|~(in @ emptyset @ X1455)|(~(in @ X1457 @ omega)|(in @ X1457 @ X1455)))&((in @ (esk4_1 @ X1455) @ X1455)|~(in @ emptyset @ X1455)|(~(in @ X1457 @ omega)|(in @ X1457 @ X1455))))&(~(in @ (setadjoin @ (esk4_1 @ X1455) @ (esk4_1 @ X1455)) @ X1455)|~(in @ emptyset @ X1455)|(~(in @ X1457 @ omega)|(in @ X1457 @ X1455))))&((((((in @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1459)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|(in @ (esk5_2 @ X1458 @ X1459) @ X1459))&((X1458 @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1464)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|(in @ (esk5_2 @ X1458 @ X1459) @ X1459)))&(~(in @ X1467 @ X1459)|~(X1458 @ X1467 @ X1466)|(in @ X1466 @ (esk7_2 @ X1458 @ X1459))|(in @ (esk5_2 @ X1458 @ X1459) @ X1459)))&(((((in @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1459)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|((X1458 @ (esk5_2 @ X1458 @ X1459) @ (esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461)))&((X1458 @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1464)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|((X1458 @ (esk5_2 @ X1458 @ X1459) @ (esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461))))&(~(in @ X1467 @ X1459)|~(X1458 @ X1467 @ X1466)|(in @ X1466 @ (esk7_2 @ X1458 @ X1459))|((X1458 @ (esk5_2 @ X1458 @ X1459) @ (esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461))))&((((in @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1459)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|(((X1461)!=(esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461)))&((X1458 @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1464)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|(((X1461)!=(esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461))))&(~(in @ X1467 @ X1459)|~(X1458 @ X1467 @ X1466)|(in @ X1466 @ (esk7_2 @ X1458 @ X1459))|(((X1461)!=(esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461))))))&((((in @ (esk9_1 @ X1468) @ X1468)|~(in @ X1469 @ X1468))&(~(in @ X1471 @ (esk9_1 @ X1468))|~(in @ X1471 @ X1468)|~(in @ X1469 @ X1468)))&((epred1_0)&((((X1472 @ (esk10_2 @ X1472 @ X1473))|~(X1472 @ X1473)|(X1472 @ (descr @ X1472)))&(((X1473)!=(esk10_2 @ X1472 @ X1473))|~(X1472 @ X1473)|(X1472 @ (descr @ X1472))))&((~(in @ X1477 @ X1475)|(~(X1476 @ X1477)|(in @ X1477 @ (dsetconstr @ X1475 @ X1476))))&((~(in @ X1480 @ (dsetconstr @ X1478 @ X1479))|(in @ X1480 @ X1478))&((~(in @ X1483 @ (dsetconstr @ X1481 @ X1482))|(X1482 @ X1483))&(((((X1484 @ (esk12_1 @ X1484))|((X1484 @ (esk11_2 @ X1484 @ X1485))|~(X1484 @ X1485)))&(~(X1484 @ X1488)|((esk12_1 @ X1484)=(X1488))|((X1484 @ (esk11_2 @ X1484 @ X1485))|~(X1484 @ X1485))))&(((X1484 @ (esk12_1 @ X1484))|(((X1485)!=(esk11_2 @ X1484 @ X1485))|~(X1484 @ X1485)))&(~(X1484 @ X1488)|((esk12_1 @ X1484)=(X1488))|(((X1485)!=(esk11_2 @ X1484 @ X1485))|~(X1484 @ X1485)))))&((~(in @ X1490 @ (prop2set @ ((X1489))))|(X1489))&((~(in @ X1491 @ emptyset)|(X1492))&((~(in @ X1493 @ emptyset)|~($true))&(~(in @ X1494 @ emptyset)&((((X1495 @ (esk13_2 @ X1495 @ X1496))|~(X1495 @ X1496)|(X1495 @ (esk14_1 @ X1495)))&(((X1496)!=(esk13_2 @ X1495 @ X1496))|~(X1495 @ X1496)|(X1495 @ (esk14_1 @ X1495))))&(((((in @ (esk16_2 @ X1499 @ X1500) @ X1500)|((X1499)=(X1500))|(in @ (esk15_2 @ X1499 @ X1500) @ X1499))&(~(in @ (esk16_2 @ X1499 @ X1500) @ X1499)|((X1499)=(X1500))|(in @ (esk15_2 @ 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X1980))|(in @ X1981 @ X1978))&((~(in @ (kpair @ X1986 @ X1987) @ (dpsetconstr @ X1983 @ X1984 @ X1985))|(in @ X1987 @ X1984))&((~(in @ (kpair @ X1991 @ X1992) @ (dpsetconstr @ X1988 @ X1989 @ X1990))|(X1990 @ X1991 @ X1992))&((((in @ (esk69_4 @ X1993 @ X1994 @ X1995 @ X1996) @ (dsetconstr @ X1994 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1996 @ Z0) @ X1995)))))|~(in @ X1996 @ X1993)|~(func @ X1993 @ X1994 @ X1995))&(((dsetconstr @ X1994 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1996 @ Z0) @ X1995))))=(setadjoin @ (esk69_4 @ X1993 @ X1994 @ X1995 @ X1996) @ emptyset))|~(in @ X1996 @ X1993)|~(func @ X1993 @ X1994 @ X1995)))&((~(func @ X1998 @ X1999 @ X2000)|(~(in @ X2001 @ X1998)|(in @ (setunion @ (dsetconstr @ X1999 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2001 @ Z0) @ X2000))))) @ X1999)))&((~(func @ X2002 @ X2003 @ X2004)|(~(in @ X2005 @ X2002)|(in @ (ap @ X2002 @ X2003 @ X2004 @ X2005) @ X2003)))&((~(in @ X2008 @ (funcSet @ X2006 @ X2007))|(func @ X2006 @ X2007 @ X2008))&((~(in @ X2011 @ (funcSet @ X2009 @ X2010))|(~(in @ X2012 @ X2009)|(in @ (ap @ X2009 @ X2010 @ X2011 @ X2012) @ X2010)))&((~(func @ X2013 @ X2014 @ X2015)|(in @ X2015 @ (funcSet @ X2013 @ X2014)))&((((in @ (esk70_3 @ X2016 @ X2017 @ X2018) @ X2016)|(func @ X2016 @ X2017 @ (dpsetconstr @ X2016 @ X2017 @ (^[Z0/* 3 */:$i]:($eq @ (X2018 @ Z0))))))&(~(in @ (X2018 @ (esk70_3 @ X2016 @ X2017 @ X2018)) @ X2017)|(func @ X2016 @ X2017 @ (dpsetconstr @ X2016 @ X2017 @ (^[Z0/* 3 */:$i]:($eq @ (X2018 @ Z0)))))))&((((in @ (esk71_3 @ X2020 @ X2021 @ X2022) @ X2020)|(func @ X2020 @ X2021 @ (lam @ X2020 @ X2021 @ X2022)))&(~(in @ (X2022 @ (esk71_3 @ X2020 @ X2021 @ X2022)) @ X2021)|(func @ X2020 @ X2021 @ (lam @ X2020 @ X2021 @ X2022))))&((((in @ (esk72_3 @ X2024 @ X2025 @ X2026) @ X2024)|(in @ (lam @ X2024 @ X2025 @ X2026) @ (funcSet @ X2024 @ X2025)))&(~(in @ (X2026 @ (esk72_3 @ X2024 @ X2025 @ X2026)) @ X2025)|(in @ (lam @ X2024 @ X2025 @ X2026) @ (funcSet @ X2024 @ X2025))))&((((in @ (esk73_4 @ X2028 @ X2029 @ X2030 @ X2031) @ X2028)|(~(in @ X2034 @ X2030)|(X2031 @ X2034))|~(subset @ X2030 @ (cartprod @ X2028 @ X2029)))&(((in @ (esk74_4 @ X2028 @ X2029 @ X2030 @ X2031) @ X2029)|(~(in @ X2034 @ X2030)|(X2031 @ X2034))|~(subset @ X2030 @ (cartprod @ X2028 @ X2029)))&(((in @ (kpair @ (esk73_4 @ X2028 @ X2029 @ X2030 @ X2031) @ (esk74_4 @ X2028 @ X2029 @ X2030 @ X2031)) @ X2030)|(~(in @ X2034 @ X2030)|(X2031 @ X2034))|~(subset @ X2030 @ (cartprod @ X2028 @ X2029)))&(~(X2031 @ (kpair @ (esk73_4 @ X2028 @ X2029 @ X2030 @ X2031) @ (esk74_4 @ X2028 @ X2029 @ X2030 @ X2031)))|(~(in @ X2034 @ X2030)|(X2031 @ X2034))|~(subset @ X2030 @ (cartprod @ X2028 @ X2029))))))&((((in @ (esk75_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2035)|(~(in @ X2041 @ X2037)|(X2038 @ X2041))|~(subset @ X2037 @ (cartprod @ X2035 @ X2036)))&(((in @ (esk76_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2036)|(~(in @ X2041 @ X2037)|(X2038 @ X2041))|~(subset @ X2037 @ (cartprod @ X2035 @ X2036)))&(((in @ (kpair @ (esk75_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk76_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2037)|(~(in @ X2041 @ X2037)|(X2038 @ X2041))|~(subset @ X2037 @ (cartprod @ X2035 @ X2036)))&(~(X2038 @ (kpair @ (esk75_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk76_4 @ X2035 @ X2036 @ X2037 @ X2038)))|(~(in @ X2041 @ X2037)|(X2038 @ X2041))|~(subset @ X2037 @ (cartprod @ X2035 @ X2036))))))&((~(in @ X2044 @ (dsetconstr @ X2042 @ X2043))|((dsetconstr @ X2042 @ X2043)!=(setadjoin @ X2044 @ emptyset))|(~(in @ X2045 @ X2042)|(~(in @ X2046 @ X2042)|(~(X2043 @ X2045)|(~(X2043 @ X2046)|((X2045)=(X2046)))))))&((~(func @ X2047 @ X2048 @ X2049)|(~(in @ X2050 @ X2047)|(in @ (kpair @ X2050 @ (ap @ X2047 @ X2048 @ X2049 @ X2050)) @ X2049)))&((~(in @ X2053 @ (funcSet @ X2051 @ X2052))|(~(in @ X2054 @ X2051)|(in @ (kpair @ X2054 @ (ap @ X2051 @ X2052 @ X2053 @ X2054)) @ X2053)))&((~(func @ X2055 @ X2056 @ X2057)|(~(in @ X2058 @ X2055)|(~(in @ X2059 @ X2056)|(~(in @ (kpair @ X2058 @ X2059) @ X2057)|((ap @ X2055 @ X2056 @ X2057 @ X2058)=(X2059))))))&((((in @ (esk77_4 @ X2060 @ X2061 @ X2062 @ X2063) @ X2060)|(~(in @ X2065 @ X2060)|(~(in @ X2066 @ X2061)|(~(in @ (kpair @ X2065 @ X2066) @ X2063)|(in @ (kpair @ X2065 @ X2066) @ X2062))))|~(func @ X2060 @ X2061 @ X2063)|~(func @ X2060 @ X2061 @ X2062))&(((ap @ X2060 @ X2061 @ X2062 @ (esk77_4 @ X2060 @ X2061 @ X2062 @ X2063))!=(ap @ X2060 @ X2061 @ X2063 @ (esk77_4 @ X2060 @ X2061 @ X2062 @ X2063)))|(~(in @ X2065 @ X2060)|(~(in @ X2066 @ X2061)|(~(in @ (kpair @ X2065 @ X2066) @ X2063)|(in @ (kpair @ X2065 @ X2066) @ X2062))))|~(func @ X2060 @ X2061 @ X2063)|~(func @ X2060 @ X2061 @ X2062)))&((~(in @ X2069 @ (funcSet @ X2067 @ X2068))|(~(in @ X2070 @ X2067)|(~(in @ X2071 @ X2068)|(~(in @ (kpair @ X2070 @ X2071) @ X2069)|((ap @ X2067 @ X2068 @ X2069 @ X2070)=(X2071))))))&((((in @ (esk78_4 @ X2072 @ X2073 @ X2074 @ X2075) @ X2072)|(subset @ X2074 @ X2075)|~(subset @ X2075 @ (cartprod @ X2072 @ X2073))|~(subset @ X2074 @ (cartprod @ X2072 @ X2073)))&(((in @ (esk79_4 @ X2072 @ X2073 @ X2074 @ X2075) @ X2073)|(subset @ X2074 @ X2075)|~(subset @ X2075 @ (cartprod @ X2072 @ X2073))|~(subset @ X2074 @ (cartprod @ X2072 @ X2073)))&(((in @ (kpair @ (esk78_4 @ X2072 @ X2073 @ X2074 @ X2075) @ (esk79_4 @ X2072 @ X2073 @ X2074 @ X2075)) @ X2074)|(subset @ X2074 @ X2075)|~(subset @ X2075 @ (cartprod @ X2072 @ X2073))|~(subset @ X2074 @ (cartprod @ X2072 @ X2073)))&(~(in @ (kpair @ (esk78_4 @ X2072 @ X2073 @ X2074 @ X2075) @ (esk79_4 @ X2072 @ X2073 @ X2074 @ X2075)) @ X2075)|(subset @ X2074 @ X2075)|~(subset @ X2075 @ (cartprod @ X2072 @ X2073))|~(subset @ X2074 @ (cartprod @ X2072 @ X2073))))))&(((((in @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|((X2080)=(X2081))|(in @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|((X2080)=(X2081))|(in @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|((X2080)=(X2081))|(in @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(~(in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|((X2080)=(X2081))|(in @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079))))))&((((in @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|((X2080)=(X2081))|(in @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|((X2080)=(X2081))|(in @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|((X2080)=(X2081))|(in @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(~(in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|((X2080)=(X2081))|(in @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079))))))&((((in @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|((X2080)=(X2081))|(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|((X2080)=(X2081))|(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|((X2080)=(X2081))|(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(~(in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|((X2080)=(X2081))|(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079))))))&(((in @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|((X2080)=(X2081))|~(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|((X2080)=(X2081))|~(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|((X2080)=(X2081))|~(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(~(in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|((X2080)=(X2081))|~(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))))))))&((((in @ (esk84_4 @ X2086 @ X2087 @ X2088 @ X2089) @ X2086)|((X2088)=(X2089))|~(func @ X2086 @ X2087 @ X2089)|~(func @ X2086 @ X2087 @ X2088))&(((ap @ X2086 @ X2087 @ X2088 @ (esk84_4 @ X2086 @ X2087 @ X2088 @ X2089))!=(ap @ X2086 @ X2087 @ X2089 @ (esk84_4 @ X2086 @ X2087 @ X2088 @ X2089)))|((X2088)=(X2089))|~(func @ X2086 @ X2087 @ X2089)|~(func @ X2086 @ X2087 @ X2088)))&((((in @ (esk85_4 @ X2091 @ X2092 @ X2093 @ X2094) @ X2091)|((X2093)=(X2094))|~(in @ X2094 @ (funcSet @ X2091 @ X2092))|~(in @ X2093 @ (funcSet @ X2091 @ X2092)))&(((ap @ X2091 @ X2092 @ X2093 @ (esk85_4 @ X2091 @ X2092 @ X2093 @ X2094))!=(ap @ X2091 @ X2092 @ X2094 @ (esk85_4 @ X2091 @ X2092 @ X2093 @ X2094)))|((X2093)=(X2094))|~(in @ X2094 @ (funcSet @ X2091 @ X2092))|~(in @ X2093 @ (funcSet @ X2091 @ X2092))))&((~(in @ X2098 @ (funcSet @ X2096 @ X2097))|(~(in @ X2099 @ X2096)|((ap @ X2096 @ X2097 @ X2098 @ X2099)=(ap @ X2096 @ X2097 @ X2098 @ X2099))))&((~(func @ X2100 @ X2101 @ X2102)|(~(in @ X2103 @ X2100)|((ap @ X2100 @ X2101 @ X2102 @ X2103)=(ap @ X2100 @ X2101 @ X2102 @ X2103))))&((((in @ (esk86_3 @ X2104 @ X2105 @ X2106) @ X2104)|(~(in @ X2108 @ X2104)|((ap @ X2104 @ X2105 @ (lam @ X2104 @ X2105 @ X2106) @ X2108)=(X2106 @ X2108))))&(~(in @ (X2106 @ (esk86_3 @ X2104 @ X2105 @ X2106)) @ X2105)|(~(in @ X2108 @ X2104)|((ap @ X2104 @ X2105 @ (lam @ X2104 @ X2105 @ X2106) @ X2108)=(X2106 @ X2108)))))&((~(func @ X2109 @ X2110 @ X2111)|((lam @ X2109 @ X2110 @ (ap @ X2109 @ X2110 @ X2111))=(X2111)))&((((in @ (esk87_3 @ X2112 @ X2113 @ X2114) @ X2112)|((lam @ X2112 @ X2113 @ X2114)=(lam @ X2112 @ X2113 @ X2114)))&(~(in @ (X2114 @ (esk87_3 @ X2112 @ X2113 @ X2114)) @ X2113)|((lam @ X2112 @ X2113 @ X2114)=(lam @ X2112 @ X2113 @ X2114))))&((((in @ (esk88_3 @ X2116 @ X2117 @ X2118) @ X2116)|(~(in @ X2120 @ X2116)|((ap @ X2116 @ X2117 @ (lam @ X2116 @ X2117 @ X2118) @ X2120)=(X2118 @ X2120))))&(~(in @ (X2118 @ (esk88_3 @ X2116 @ X2117 @ X2118)) @ X2117)|(~(in @ X2120 @ X2116)|((ap @ X2116 @ X2117 @ (lam @ X2116 @ X2117 @ X2118) @ X2120)=(X2118 @ X2120)))))&((~(in @ X2123 @ (funcSet @ X2121 @ X2122))|((lam @ X2121 @ X2122 @ (ap @ X2121 @ X2122 @ X2123))=(X2123)))&((in @ esk90_0 @ esk89_0)&((in @ esk91_0 @ esk89_0)&(~(epred2_0)&~(in @ esk91_0 @ (dsetconstr @ esk89_0 @ (^[Z0/* 9 */:$i]:(((((Z0)=(esk90_0))&(epred2_0))|(((Z0)=(esk91_0))&~((epred2_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_305])])])])])])])). 1.04/3.17 thf(c_0_307, plain, ![X2147:$i]:(((epred3_0 @ X2147)<=>((((X2147)=(esk90_0))&(epred2_0))|(((X2147)=(esk91_0))&~((epred2_0)))))), introduced(definition)). 1.04/3.17 thf(c_0_308, plain, ![X2158:$i]:(((((((X2158)=(esk91_0))|((X2158)=(esk90_0))|~(epred3_0 @ X2158))&(~(epred2_0)|((X2158)=(esk90_0))|~(epred3_0 @ X2158)))&((((X2158)=(esk91_0))|(epred2_0)|~(epred3_0 @ X2158))&(~(epred2_0)|(epred2_0)|~(epred3_0 @ X2158))))&((((X2158)!=(esk90_0))|~(epred2_0)|(epred3_0 @ X2158))&(((X2158)!=(esk91_0))|(epred2_0)|(epred3_0 @ X2158))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])])). 1.04/3.17 thf(c_0_309, negated_conjecture, ~((((in @ esk91_0 @ (dsetconstr @ esk89_0 @ epred3_0)))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_306]), c_0_307])). 1.04/3.17 thf(c_0_310, plain, ![X2:$i]:(((epred2_0)|(epred3_0 @ X2)|((X2)!=(esk91_0)))), inference(split_conjunct,[status(thm)],[c_0_308])). 1.04/3.17 thf(c_0_311, negated_conjecture, ~((epred2_0)), inference(split_conjunct,[status(thm)],[c_0_306])). 1.04/3.17 thf(c_0_312, negated_conjecture, ~((in @ esk91_0 @ (dsetconstr @ esk89_0 @ epred3_0))), inference(cn,[status(thm)],[c_0_309])). 1.04/3.17 thf(c_0_313, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_306])). 1.04/3.17 thf(c_0_314, negated_conjecture, (in @ esk91_0 @ esk89_0), inference(split_conjunct,[status(thm)],[c_0_306])). 1.04/3.17 thf(c_0_315, plain, (epred3_0 @ esk91_0), inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_310, c_0_311])])). 1.04/3.17 thf(c_0_316, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_312, c_0_313]), c_0_314]), c_0_315])]), ['proof']). 1.04/3.17 # SZS output end CNFRefutation 1.04/3.17 # Parsed axioms : 475 1.04/3.17 # Removed by relevancy pruning/SinE : 0 1.04/3.17 # Initial clauses : 673 1.04/3.17 # Removed in clause preprocessing : 286 1.04/3.17 # Initial clauses in saturation : 387 1.04/3.17 # Processed clauses : 636 1.04/3.17 # ...of these trivial : 12 1.04/3.17 # ...subsumed : 66 1.04/3.17 # ...remaining for further processing : 558 1.04/3.17 # Other redundant clauses eliminated : 26 1.04/3.17 # Clauses deleted for lack of memory : 0 1.04/3.17 # Backward-subsumed : 0 1.04/3.17 # Backward-rewritten : 5 1.04/3.17 # Generated clauses : 1356 1.04/3.17 # ...of the previous two non-redundant : 1227 1.04/3.17 # ...aggressively subsumed : 0 1.04/3.17 # Contextual simplify-reflections : 1 1.04/3.17 # Paramodulations : 1305 1.04/3.17 # Factorizations : 0 1.04/3.17 # NegExts : 9 1.04/3.17 # Equation resolutions : 29 1.04/3.17 # Disequality decompositions : 0 1.04/3.17 # Total rewrite steps : 151 1.04/3.17 # ...of those cached : 97 1.04/3.17 # Propositional unsat checks : 0 1.04/3.17 # Propositional check models : 0 1.04/3.17 # Propositional check unsatisfiable : 0 1.04/3.17 # Propositional clauses : 0 1.04/3.17 # Propositional clauses after purity: 0 1.04/3.17 # Propositional unsat core size : 0 1.04/3.17 # Propositional preprocessing time : 0.000 1.04/3.17 # Propositional encoding time : 0.000 1.04/3.17 # Propositional solver time : 0.000 1.04/3.17 # Success case prop preproc time : 0.000 1.04/3.17 # Success case prop encoding time : 0.000 1.04/3.17 # Success case prop solver time : 0.000 1.04/3.17 # Current number of processed clauses : 196 1.04/3.17 # Positive orientable unit clauses : 49 1.04/3.17 # Positive unorientable unit clauses: 0 1.04/3.17 # Negative unit clauses : 5 1.04/3.17 # Non-unit-clauses : 142 1.04/3.17 # Current number of unprocessed clauses: 1311 1.04/3.17 # ...number of literals in the above : 3568 1.04/3.17 # Current number of archived formulas : 0 1.04/3.17 # Current number of archived clauses : 347 1.04/3.17 # Clause-clause subsumption calls (NU) : 20033 1.04/3.17 # Rec. Clause-clause subsumption calls : 6760 1.04/3.17 # Non-unit clause-clause subsumptions : 41 1.04/3.17 # Unit Clause-clause subsumption calls : 161 1.04/3.17 # Rewrite failures with RHS unbound : 0 1.04/3.17 # BW rewrite match attempts : 25 1.04/3.17 # BW rewrite match successes : 3 1.04/3.17 # Condensation attempts : 0 1.04/3.17 # Condensation successes : 0 1.04/3.17 # Termbank termtop insertions : 85943 1.04/3.17 # Search garbage collected termcells : 22931 1.04/3.17 1.04/3.17 # ------------------------------------------------- 1.04/3.17 # User time : 0.099 s 1.04/3.17 # System time : 0.014 s 1.04/3.17 # Total time : 0.113 s 1.04/3.17 # Maximum resident set size: 7380 pages 1.04/3.17 1.04/3.17 # ------------------------------------------------- 1.04/3.17 # User time : 0.195 s 1.04/3.17 # System time : 0.029 s 1.04/3.17 # Total time : 0.224 s 1.04/3.17 # Maximum resident set size: 2412 pages 1.04/3.17 % E---3.1 exiting 1.04/3.19 % E exiting 1.04/3.19 EOF